$$U_{771}(x, y) = \frac{2 \sqrt{3} \left(\frac{2 \sqrt{3} x \sin{\left(\frac{\arcsin{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)}}{3 \sqrt{y}} + 1\right)^{2} \sin{\left(\frac{\arcsin{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)}}{3 \sqrt{y}}$$

$$T_{771}(n, m, k) = \frac{\left(k + n\right) {\binom{2 k}{n}} {\binom{k + 3 m + n - 1}{m}}}{k + 2 m + n}$$